I wonder if one could somehow temporarily disable the magnetic stripe? I wouldn't dare scratch it off completely, but I would love to cover it up as a precaution.
You could always get hold of a card reader/writer and do it your self. The magstripe is essentially just a small capacity magnetic disk. You can read the information off and store it, then proceed to wipe it clean. If you want to restore, just write the data back.
It's not that easy, there are High Coercivity and Low Coercivity magstripes. HiCo cards need special writers because they're more resistant to external magnetic fields.